Dear Mr. DavisThank you for your email. Apart from the name and birth place of the father, which was detailed on forms completed by members at the time of their matriculation ‎(ie when they were admitted to the University)‎, Oxford University Archives does not hold information on the families of its members. I have checked Joseph Foster's 'Alumni Oxonienses', a printed register of all those who matriculated between 1500 and 1714, and the entry for William Davis, which confirms the details given in your email, is as follows:

William Davis was the son of William Davis a plebeian of Llanstephan, Radnorshire. He matriculated from St Mary Hall on 30 June 1682, aged 18.

The Oxford Colleges maintain their own archives and it is possible that Oriel College, which holds the records of St Mary Hall, may hold additional information on William Davis. Rob Petre, the Oriel College Archivist, can be contacted at <archives@oriel.ox.ac.uk <mailto:archives@oriel.ox.ac.uk>>.